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The eTCL code could either use the raw trailing edge concept or select from a list of known trailing edge factors in the limited tablet problems available. There are instances where the Bablylonian tablets are splitting off more than one power as the end factor. A prime number is prime in any base, so it may be inferred that the trailing edges of 7 and 17 would not be factorable in base 10. The numbers 7 and 17 are prime numbers and their trailing edges are not factorable by 2,2,3,5 in base 60. In base 60, 2.5 (decimal 125) has trailing edge of 5 and is factorable by 5. Meaning that the regular Bablylonian numbers that have end digits of 2/2/3/5 should be factorable by 2/2/3/5, at least. For the Babylonian base 60, the prime factors are 2/2/3/5. The number 24 is 2*3*4 and factorable by 4, but 14 is 2*7, not factorable by 4. There are instances of end digits in base 10, where the trailing edge works occasionally, but not completely. The number 125 is 5*5*5, factorable by 5. For example, the number 12 is 2*3*3, factorable by 2. The base 10 has factors 2*5 and numbers ending in 2/5 should be factorable by 2 or 5 respectively. The following discussion assumes that the numbers are written left to right, decreasing powers of selected base on right. Both the trailing edge algorithm and the reverse sequence algorithm have parallels to the Babylonian square root algorithm.įor the trailing edge concept, the number in specific base should have end digits on the trailing edge as factors of the base. There are features in the tablet display or factor selection that suggest that the reverse sequence algorithm is a didactic or expository work. The reverse sequence algorithm is the inverse reciprocal or constructs a number from a known reciprocal, usually a reciprocal generated from previous use of trailing edge algorithm. The trailing edge algorithm is defined as the method used by scribes to successively factor a number to produce reciprocals. The Babylonians did not use algebra notation, so the reader will have to bear some anachronisms in the eTCL pseudocode. In many cases, the Babylonians cited a reciprocal on a clay tablet, but the derivation or algorithm was not marked or known.

This work is a follow on to the Babylonian irregular reciprocal calculator, but this wiki page places more emphasis on the number properties and the multiple algorithms for reciprocals in Babylonian use. The Babylonian trailing edge algorithm and reverse sequence algorithm from clay tablets was loaded into an eTCL calculator. Then the eTCL calculator can be run over a number of testcases to validate the algebraic equations. At least one approach for the modern reader and using modern terminology is to develop the implied algebraic equations and decimal equivalents from the cuneiform numbers. On the particular algorithms that use factoring, the relative value or uncertain magnitude makes a big difference because the factors of 20 and 1/20 are not the same. The basic dimensions and final tallies were presented in the cuneiform accounts on clay tablets, but some calculations and some units were left off the tablet. In cuneiform, numbers in base 60 are written using a relative notation. One difficulty is determining the effective magnitude or power of the number coefficient in the base 60 notation. In most cases, the math problem is how the coefficient was used in estimating materials, work rates, and math problems. In the cuneiform math problems and coefficient lists on clay tablets, there are coefficient numbers which were used in determining the amount of materials and the daily work rates of the workers. Additional console programs below are used to check or improve subroutine. Gold Here is some eTCL starter code for Babylonian trailing edge algorithm and reverse sequence algorithm for reciprocals in calculator shell.

Its very hard to reply reasonably without some background of the correspondent on his WIKI bio page. Aside from your courtesy, your wiki MONIKER and date as a signature and minimal good faith of any internet post are the rules of this TCL-WIKI. Please include your wiki MONIKER and date in your comment with the same courtesy that I will give you. Comments are welcome, but please load any comments in the comments section at the bottom of the page. Console program for reverse_sequence_reciprocal algorithmīabylonian trailing edge algorithm and reverse sequence algorithm for reciprocals, eTCL demo example calculator, numerical analysis.Console program for trailing edge reciprocal algorithm.Testcase 6 for decimal 1296000., base10.Babylonian trailing edge algorithm and reverse sequence algorithm for reciprocals, eTCL demo example calculator, numerical analysis.

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